Polytope of Type {3,2,6,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,22}*1584
if this polytope has a name.
Group : SmallGroup(1584,675)
Rank : 5
Schlafli Type : {3,2,6,22}
Number of vertices, edges, etc : 3, 3, 6, 66, 22
Order of s₀s₁s₂s₃s₄ : 66
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,2,22}*528
   6-fold quotients : {3,2,2,11}*264
   11-fold quotients : {3,2,6,2}*144
   22-fold quotients : {3,2,3,2}*72
   33-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)(24,35)
(25,36)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)
(58,69);;
s3 := ( 4,15)( 5,25)( 6,24)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)
(14,16)(27,36)(28,35)(29,34)(30,33)(31,32)(37,48)(38,58)(39,57)(40,56)(41,55)
(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(60,69)(61,68)(62,67)(63,66)
(64,65);;
s4 := ( 4,38)( 5,37)( 6,47)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,41)(13,40)
(14,39)(15,49)(16,48)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)
(25,50)(26,60)(27,59)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)
(36,61);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(69)!(2,3);
s1 := Sym(69)!(1,2);
s2 := Sym(69)!(15,26)(16,27)(17,28)(18,29)(19,30)(20,31)(21,32)(22,33)(23,34)
(24,35)(25,36)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)
(57,68)(58,69);
s3 := Sym(69)!( 4,15)( 5,25)( 6,24)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)
(13,17)(14,16)(27,36)(28,35)(29,34)(30,33)(31,32)(37,48)(38,58)(39,57)(40,56)
(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)(60,69)(61,68)(62,67)(63,66)
(64,65);
s4 := Sym(69)!( 4,38)( 5,37)( 6,47)( 7,46)( 8,45)( 9,44)(10,43)(11,42)(12,41)
(13,40)(14,39)(15,49)(16,48)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)
(24,51)(25,50)(26,60)(27,59)(28,69)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)
(35,62)(36,61);
poly := sub<Sym(69)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope